High-order adiabatic approximations related to non-Abelian Berry's phase factors and nuclear quadrupole resonance

Chang-Pu Sun

doi:10.1103/PhysRevD.41.1318

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High-order adiabatic approximations related to non-Abelian Berry's phase factors and nuclear quadrupole resonance

Chang-Pu Sun^*

Chinese Center of Advanced Science and Technology (World Laboratory) [CCAST], P.O. Box 8730, Beijing, People's Republic of China
Physics Department, Northeast Normal University, Changchun, Jilin Province, People's Republic of China

^*Present mailing address: Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin, People's Republic of China.

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Phys. Rev. D 41, 1318 – Published 15 February, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.1318

Abstract

A high-order adiabatic-approximation method is proposed to study the time evolution of degenerate quantum-mechanical systems with slowly changing Hamiltonians. We not only discuss the quantum adiabatic theorem, induced gauge structure, and non-Abelian Berry's phase factors in the first-order approximation, but we also give nonadiabatic corrections for problems in the second-order approximation. With the nuclear quadrupole resonance as an explicit example, we analyze the above-mentioned questions in detail and point out the observable effects of non-Abelian Berry's phase factors for nonadiabatic transitions between two instantaneous states in an improvement of Tycko's experiment.

References (18)

M. V. Berry, Proc. R. Soc. London A392, 45 (1984)
R. Jackiw, Comments Atom. Mol. Phys. 21, 71 (1988)
R. Tycko, Phys. Rev. Lett. 58, 2281 (1987)
D. J. Richardson et al., Phys. Rev. Lett. 61, 2030 (1988)
M. V. Berry, Proc. R. Soc. London A414, 47 (1987)
N. Nakagawa, Ann. Phys. (N.Y.) 179, 145 (1987)
C.-P. Sun, J. Phys. A 21, 1595 (1988)
C.-P. Sun, High Energy Phys. Nucl. Phys. 12, 352 (1988)
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C.-P. Sun, Chin. Phys. Lett. 6, 97 (1989)
C.-P. Sun, Phys. Rev. D 38, 2908 (1988)
C.-P. Sun, High Energy Phys. Nucl. Phys. 13, 403 (1989)
C.-P. Sun, High Energy Phys. Nucl. Phys. 13, 109 (1989)
F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984)
A. Zee, Phys. Rev. A 38, 1 (1988)
J. Moody et al., Phys. Rev. Lett. 59, 161 (1987)
J. Segert, Ann. Phys. (N.Y.) 179, 294 (1987)
B. Simon, Phys. Rev. Lett. 51, 2167 (1983)

[c1] M. V. Berry, Proc. R. Soc. London A392, 45 (1984)

[c2] R. Jackiw, Comments Atom. Mol. Phys. 21, 71 (1988)

[c3] R. Tycko, Phys. Rev. Lett. 58, 2281 (1987)

[c4] D. J. Richardson et al., Phys. Rev. Lett. 61, 2030 (1988)

[c5] M. V. Berry, Proc. R. Soc. London A414, 47 (1987)

[c6] N. Nakagawa, Ann. Phys. (N.Y.) 179, 145 (1987)

[c7] C.-P. Sun, J. Phys. A 21, 1595 (1988)

[c8] C.-P. Sun, High Energy Phys. Nucl. Phys. 12, 352 (1988)

[c9] N. Papanicolaou, J. Phys. (Paris) 49, 1493 (1988)

[c10] C.-P. Sun, Chin. Phys. Lett. 6, 97 (1989)

[c11] C.-P. Sun, Phys. Rev. D 38, 2908 (1988)

[c12] C.-P. Sun, High Energy Phys. Nucl. Phys. 13, 403 (1989)

[c13] C.-P. Sun, High Energy Phys. Nucl. Phys. 13, 109 (1989)

[c14] F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984)

[c15] A. Zee, Phys. Rev. A 38, 1 (1988)

[c16] J. Moody et al., Phys. Rev. Lett. 59, 161 (1987)

[c17] J. Segert, Ann. Phys. (N.Y.) 179, 294 (1987)

[c18] B. Simon, Phys. Rev. Lett. 51, 2167 (1983)

Physical Review D

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High-order adiabatic approximations related to non-Abelian Berry's phase factors and nuclear quadrupole resonance

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References (18)

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